dynamic_2d_nonlinear_solve
Analyzes nonlinear 2D ODE systems, identifying equilibria, classifying stability via Jacobian, and generating nullclines and trajectories for phase portraits.
Instructions
Solve and analyze the nonlinear 2D system x' = f(x,y), y' = g(x,y).
Args: eq_x, eq_y: Math expressions for f and g (variables x, y, mu and extra params). params: extra parameter values (e.g. {'alpha': 0.5}). mu: bifurcation parameter value. x0..y_max, cantidad_trayectorias: integration and portrait settings.
Returns: Dict with equilibria, Jacobian-based classification, nullclines and trajectories.
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| h | No | ||
| mu | No | ||
| t0 | No | ||
| x0 | No | ||
| y0 | No | ||
| eq_x | No | y - x | |
| eq_y | No | x**2 - 1 | |
| t_fin | No | ||
| x_max | No | ||
| x_min | No | ||
| y_max | No | ||
| y_min | No | ||
| params | No | ||
| cantidad_trayectorias | No |